We have proposed an efficient, \(h-\) adaptive IMEX-DG solver for the compressible Naiver-Stokes equations
with general equation of state. The solver combines ideas from the discretization approaches in [1]}, [2]}, [3]}, [4]}
and proposes an improvement in the choice of the free parameter employed by the explicit part of the IMEX scheme described in [3]}. The resulting method achieves full second order accuracy also including viscous terms and implements an \(h-\) adaptive approach in the framework of the numerical library deal.II. A number of physically based adaptation criteria have been proposed, which allow to exploit the full efficiency of the adaptive technique also for real gas simulations. A number of numerical experiments validate the proposed method and show its potential for low Mach number problems. In future work, we plan to extend the scheme to multiphase flows and to demonstrate its potential for application to atmospheric flows.
